Rewrite as a simplified fraction. ${0.7\overline{84} = {?}}$
Answer: Let $x$ equal the decimal. Set up two equations such that the digits after the decimal point are identical. ${\begin{align*}1000x &= 784.8484...\\ 10x &= 7.8484...\end{align*}}$ Subtracting the two equations, we have: ${990x = 777}$ ${x = \dfrac{777}{990}} $ ${x = \dfrac{259}{330}} $